## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$3x^{}b\sqrt[3]{x^2}$
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the given expression is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{3x^4b}\sqrt[3]{9xb^2} \\\\= \sqrt[3]{3x^4b(9xb^2)} \\\\= \sqrt[3]{27x^{4+1}b^{1+2}} \\\\= \sqrt[3]{27x^{5}b^{3}} .\end{array} Extracting the factors that are perfect powers of the index, the given expression simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{27x^{5}b^{3}} \\\\= \sqrt[3]{27x^{3}b^{3}\cdot x^2} \\\\= \sqrt[3]{(3x^{}b)^{3}\cdot x^2} \\\\= 3x^{}b\sqrt[3]{x^2} .\end{array}